Polynomials Class 10 Maths - Division Algorithm For Polynomials

Polynomials Class 10 Maths - Division Algorithm For Polynomials

If p(x) and g(x) are any two polynomials with g(x)0 then we can find the polynomials q(x) and r(x) such that i.e. p(x) =g(x)q(x) +r(x) where r(x)=0 or degree of r(x) is less than degree of g(x). This is called division algorithm.

Step 1: arrange the dividend and divisor with decreasing order of their degrees.
Step 2: divide the highest degree term in dividend by highest degree term of divisor
Step 3: Check the degree of remainder, if it is less than the divisor then process ends. if it is greater than or equal to divisor then divide it till the highest degree in remainder less than highest degree in divisor.
Step 4: Dividing again we get quotient q(x) =3x-5 and remainder r(x) =9x+10. now the highest degree in remainder is less than highest degree in divisor hence we can not continue the division process further.

Verification of division algorithm:
We can verify if the division algorithm as
Dividend = Divisor Quotient +Remainder